Here you will find lines practice problems which is also known as linear functions. Your understanding of lines will be helpful when studying Caluclus. Visit this page directly at hunkim.com/lines
- In what quadrants is the line y=3x+2 found?
SolutionI, II, III
Video - Find the slope of y=5-3x
Solution - Find the y-intercept of y=2x+5
Solution - Find the x-intercept of 3x-4y=1
Solution - Find the y-intercept of \frac{2x}{3}-\frac{3y}{5}=\frac{1}{2}
Solution - What slope is perpendicular to m=-\frac{3}{4}?
Solution - What is the slope of the line x=0?
SolutionUndefined
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Slope is undefined (vertical line) - What is the slope of the line y=-1?
Solution - What is the slope of the line y=x?
Solution - Given y=2x+5, is the point (3,11) on this line?
SolutionYes
Video - Given 3y-x=2, is the point (2,3) on this line?
SolutionNo
Video - Find the slope given the points A(2,-2) and B(5,-17)
Solution - Given 3y=2-5x, when y=2, solve x
Solution - Find the slope in the diagram below:
Solution - See diagram below. When x=10, what is the value of y?
Solution - A line contains the points (2,5) and (6,17)
True or False: These points are found on the line y-2=3(x-1)
SolutionTrue
Video - A line contains the points (2,5) and (6,17)
The equation of the line is y=mx+b. Find b
Solution - 3-\frac{2}{3}x=6y can be written in the general equation form
Ax+By+C=0, A>0 and A, B, C\in \mathbb{Z}. Find A
Solution2
Video - 6, 9, 12, ... Find the value of the 1000th number
Solution - Does the following table represent points on a line?
SolutionYes
Video - Find the missing value in the table below:
Solution - How long is this line segment?
Solution5 - True or False: y=\frac{-2}{3}x+\frac{1}{5} is the same line as y=\frac{2}{-3}x+0.2
SolutionTrue - 4y-\frac{2}{3}x=5. Write the equation in standard form: Ax+By=C. A, B, C\in\mathbb{Z} and A>0
Solution2x-12y=-15 - Line L_1 is parallel to L_2. L_1=3x-2. Find L_2 in the form y=mx+b if it goes through the point (1,5)
Solutiony=3x+2 - Line L_1 is perpendicular to L_2. If L_1=\frac{2}{3}x+1 find the equation of L_2 in the form y=mx+b if it has an x-intercept of 3
Solutiony=\frac{-3}{2}x+\frac{9}{2} - Point: A(2,7) and B(a,3a). Given the slope is 2, find a.
Solution3 - Equation of the Line A below in the form y=mx+b?
Solutiony=-2x+4 - Equation of Line B below in the form y=mx+b?
Solutiony=\frac{1}{2}x+3 - Draw a line through the points in the gas-time graph below:
- Extrapolate the time when you run out of gas?
Solutiont=22 - If you gas tank is full at t=0, what percent of your tank is full at t=5?
Solution\approx77.3% - What is the meaning of the slope of this graph?
SolutionFuel efficiency (the rate of change of gas with respect to time)
- Extrapolate the time when you run out of gas?
- Consider the pattern 5, 8, 11, 14, …
- The variable f represents the figure number. Figure 1 contains the number 5 and figure 2 contains the number 8 and so on. Find the equation n=af+b, where n represents the number at a particular figure number.
Solutionf=3f+2 - Find the 100th number.
Solution302
- The variable f represents the figure number. Figure 1 contains the number 5 and figure 2 contains the number 8 and so on. Find the equation n=af+b, where n represents the number at a particular figure number.
- See figures 1 to 4 below. Figure 1 has 2 squares and figure 4 has 11 squares. How many squares are in figure 43?
Solution128 - Does the following table of values represent points on a line?
SolutionNo - Money is a function of time in hours: M(t)=20t+50.
- How much do you get paid for working 0 hours?
Solution\$50 - How much do you get paid if you work for 8 hours?
Solution\$210 - How many hours do you have to work to earn $280? Assume there is no overtime pay.
Solution11.5 hours
- How much do you get paid for working 0 hours?
- A line has a y-intercept of 2 and goes through the point (6,4). Find the equation of this line in slope-intercept form.
Solutiony-2=\frac{1}{3}(x-0) or y-4=\frac{1}{3}(x-6) - f(x)=\pi x+0.2. g(x) goes through the origin and never intersects with f(x). What is the equation of g(x)?
Solutiong(x)=\pi x - f(x)=3x-2. g(x)=3x+5. How many units up should we shift f(x) up in order to make the lines coincidental (infinite solutions).
Solution7 - The following table of values represents a line. Find the missing value below:
Solution24 - How many solutions? Solve the system of equations:
x+y=2 and 2y=4-2x
Solution\infty - f(x)=2x and g(x)=2+x-1+x
Solve f(x)=g(x)
SolutionNo solution - Is (1,5) a point of intersection for the system:
x+2y=13 and 3x-y=-3?
SolutionNo - Is (1,6) a point of intersection for the system:
x+2y=13 and 3x-y=-3?
SolutionYes - x+y=2 and y=3
- Solve by graphing
- Use substitution to find the coordinates of the point of intersection
Solution(-1,3)
- Solve by graphing
- 2x+3y=12 and 2y=8+4x
- Solve by using graphing
Solution - Use substitution to find the coordinates of the point of intersection
Solution(0,4) - Use elimination to find the coordinates of the point of intersection
Solution(0,4)
- Solve by using graphing
- Systems of equations word problems:
- You have 4 more cookies than your friend. You and your friend have 18 cookies combined. How many cookies do you have?
Solution11 - You have a total of 20 bills which consist of $10 and $5 bills. How many $10 bills do you have if the total value of your money is $140?
Solution8 - 3 nuts and 2 bolts weigh 12 kg and 2 nuts minus 3 bolts weigh 5 kg. How heavy is one bolt in grams?
Solution692
- You have 4 more cookies than your friend. You and your friend have 18 cookies combined. How many cookies do you have?
- Challenge:
- Line L_2 is the inverse of L_1. Given L_1 has a slope of \frac{3}{2}, find the slope of L_2.
Solution\frac{2}{3} - The cost to insure jewellery is a fixed amount plus a percentage of the value of the jewellery. It costs $32 to insure $1000 worth of jewellery or $44.50 to insure $3500 worth of jewellery. What is the fixed amount to insure jewellery?
Solution27 - An airplane travels 1600 km in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air?
Solution360 - How many ounces of 20% hydrochloric acid solution and 70% hydrochloric acid solution must be mixed to obtain 20 ounces of 50% hydrochloric acid solution?
Solution8 oz. weak acid and 12 oz. strong acid - f(x)=2-\frac{x}{2}. What is the minimum distance between this point and the point (5,2)?
Solution\sqrt{5}
- Line L_2 is the inverse of L_1. Given L_1 has a slope of \frac{3}{2}, find the slope of L_2.